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template_lapack_lanst.h
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1 /* Ergo, version 3.8, a program for linear scaling electronic structure
2  * calculations.
3  * Copyright (C) 2019 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
4  * and Anastasia Kruchinina.
5  *
6  * This program is free software: you can redistribute it and/or modify
7  * it under the terms of the GNU General Public License as published by
8  * the Free Software Foundation, either version 3 of the License, or
9  * (at your option) any later version.
10  *
11  * This program is distributed in the hope that it will be useful,
12  * but WITHOUT ANY WARRANTY; without even the implied warranty of
13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14  * GNU General Public License for more details.
15  *
16  * You should have received a copy of the GNU General Public License
17  * along with this program. If not, see <http://www.gnu.org/licenses/>.
18  *
19  * Primary academic reference:
20  * Ergo: An open-source program for linear-scaling electronic structure
21  * calculations,
22  * Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
23  * Kruchinina,
24  * SoftwareX 7, 107 (2018),
25  * <http://dx.doi.org/10.1016/j.softx.2018.03.005>
26  *
27  * For further information about Ergo, see <http://www.ergoscf.org>.
28  */
29 
30  /* This file belongs to the template_lapack part of the Ergo source
31  * code. The source files in the template_lapack directory are modified
32  * versions of files originally distributed as CLAPACK, see the
33  * Copyright/license notice in the file template_lapack/COPYING.
34  */
35 
36 
37 #ifndef TEMPLATE_LAPACK_LANST_HEADER
38 #define TEMPLATE_LAPACK_LANST_HEADER
39 
40 
41 template<class Treal>
42 Treal template_lapack_lanst(const char *norm, const integer *n, const Treal *d__, const Treal *e)
43 {
44 /* -- LAPACK auxiliary routine (version 3.0) --
45  Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
46  Courant Institute, Argonne National Lab, and Rice University
47  February 29, 1992
48 
49 
50  Purpose
51  =======
52 
53  DLANST returns the value of the one norm, or the Frobenius norm, or
54  the infinity norm, or the element of largest absolute value of a
55  real symmetric tridiagonal matrix A.
56 
57  Description
58  ===========
59 
60  DLANST returns the value
61 
62  DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm'
63  (
64  ( norm1(A), NORM = '1', 'O' or 'o'
65  (
66  ( normI(A), NORM = 'I' or 'i'
67  (
68  ( normF(A), NORM = 'F', 'f', 'E' or 'e'
69 
70  where norm1 denotes the one norm of a matrix (maximum column sum),
71  normI denotes the infinity norm of a matrix (maximum row sum) and
72  normF denotes the Frobenius norm of a matrix (square root of sum of
73  squares). Note that max(abs(A(i,j))) is not a matrix norm.
74 
75  Arguments
76  =========
77 
78  NORM (input) CHARACTER*1
79  Specifies the value to be returned in DLANST as described
80  above.
81 
82  N (input) INTEGER
83  The order of the matrix A. N >= 0. When N = 0, DLANST is
84  set to zero.
85 
86  D (input) DOUBLE PRECISION array, dimension (N)
87  The diagonal elements of A.
88 
89  E (input) DOUBLE PRECISION array, dimension (N-1)
90  The (n-1) sub-diagonal or super-diagonal elements of A.
91 
92  =====================================================================
93 
94 
95  Parameter adjustments */
96  /* Table of constant values */
97  integer c__1 = 1;
98 
99  /* System generated locals */
100  integer i__1;
101  Treal ret_val, d__1, d__2, d__3, d__4, d__5;
102  /* Local variables */
103  integer i__;
104  Treal scale;
105  Treal anorm;
106  Treal sum;
107 
108 
109  --e;
110  --d__;
111 
112  /* Initialization added by Elias to get rid of compiler warnings. */
113  anorm = 0;
114  /* Function Body */
115  if (*n <= 0) {
116  anorm = 0.;
117  } else if (template_blas_lsame(norm, "M")) {
118 
119 /* Find max(abs(A(i,j))). */
120 
121  anorm = (d__1 = d__[*n], absMACRO(d__1));
122  i__1 = *n - 1;
123  for (i__ = 1; i__ <= i__1; ++i__) {
124 /* Computing MAX */
125  d__2 = anorm, d__3 = (d__1 = d__[i__], absMACRO(d__1));
126  anorm = maxMACRO(d__2,d__3);
127 /* Computing MAX */
128  d__2 = anorm, d__3 = (d__1 = e[i__], absMACRO(d__1));
129  anorm = maxMACRO(d__2,d__3);
130 /* L10: */
131  }
132  } else if (template_blas_lsame(norm, "O") || *(unsigned char *)
133  norm == '1' || template_blas_lsame(norm, "I")) {
134 
135 /* Find norm1(A). */
136 
137  if (*n == 1) {
138  anorm = absMACRO(d__[1]);
139  } else {
140 /* Computing MAX */
141  d__3 = absMACRO(d__[1]) + absMACRO(e[1]), d__4 = (d__1 = e[*n - 1], absMACRO(
142  d__1)) + (d__2 = d__[*n], absMACRO(d__2));
143  anorm = maxMACRO(d__3,d__4);
144  i__1 = *n - 1;
145  for (i__ = 2; i__ <= i__1; ++i__) {
146 /* Computing MAX */
147  d__4 = anorm, d__5 = (d__1 = d__[i__], absMACRO(d__1)) + (d__2 = e[
148  i__], absMACRO(d__2)) + (d__3 = e[i__ - 1], absMACRO(d__3));
149  anorm = maxMACRO(d__4,d__5);
150 /* L20: */
151  }
152  }
153  } else if (template_blas_lsame(norm, "F") || template_blas_lsame(norm, "E")) {
154 
155 /* Find normF(A). */
156 
157  scale = 0.;
158  sum = 1.;
159  if (*n > 1) {
160  i__1 = *n - 1;
161  template_lapack_lassq(&i__1, &e[1], &c__1, &scale, &sum);
162  sum *= 2;
163  }
164  template_lapack_lassq(n, &d__[1], &c__1, &scale, &sum);
165  anorm = scale * template_blas_sqrt(sum);
166  }
167 
168  ret_val = anorm;
169  return ret_val;
170 
171 /* End of DLANST */
172 
173 } /* dlanst_ */
174 
175 #endif
template_blas_sqrt
Treal template_blas_sqrt(Treal x)
absMACRO
#define absMACRO(x)
Definition: template_blas_common.h:47
template_lapack_lanst
Treal template_lapack_lanst(const char *norm, const integer *n, const Treal *d__, const Treal *e)
Definition: template_lapack_lanst.h:42
template_lapack_lassq
int template_lapack_lassq(const integer *n, const Treal *x, const integer *incx, Treal *scale, Treal *sumsq)
Definition: template_lapack_lamch.h:73
template_blas_lsame
logical template_blas_lsame(const char *ca, const char *cb)
Definition: template_blas_common.cc:46
integer
int integer
Definition: template_blas_common.h:40
maxMACRO
#define maxMACRO(a, b)
Definition: template_blas_common.h:45